Simplify : x2n+3 .x(2n+1)(n+2)/(x3)2n+1 .xn(2n+1)
Answers
Answer:
Let us know some indices rules first:
\quad\quad • a^{b}*a^{c}=a^{b+c}a
b
∗a
c
=a
b+c
\quad\quad • a^{b}/a^{c}=a^{b-c}a
b
/a
c
=a
b−c
\quad\quad • (a^{b})^{c}=a^{bc}(a
b
)
c
=a
bc
Now we solve the problem:
\therefore \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}∴
(x
3
)
2n+1
.x
n(2n+1)
x
2n+3
.x
(2n+1)(n+2)
=\dfrac{x^{2n+3+(2n+1)(n+2)}}{x^{6n+3+n(2n+1)}}=
x
6n+3+n(2n+1)
x
2n+3+(2n+1)(n+2)
=\dfrac{x^{2n+3+2n^{2}+5n+2}}{x^{6n+3+2n^{2}+n}}=
x
6n+3+2n
2
+n
x
2n+3+2n
2
+5n+2
=\dfrac{x^{2n^{2}+7n+5}}{x^{2n^{2}+7n+3}}=
x
2n
2
+7n+3
x
2n
2
+7n+5
=x^{2n^{2}+7n+5-2n^{2}-7n-3}=x
2n
2
+7n+5−2n
2
−7n−3
=x^{2}=x
2
\Rightarrow \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}=x^{2}⇒
(x
3
)
2n+1
.x
n(2n+1)
x
2n+3
.x
(2n+1)(n+2)
=x
2
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